Decomposition of multicomponent mass spectra using Bayesian probability theory.

We present a method for the decomposition of the mass spectra of mixed gases using Bayesian probability theory. The method works without any calibration measurement and therefore applies also to the analysis of spectra containing unstable species. For the example of mixtures of three different hydrocarbon gases the algorithm provides concentrations and cracking coefficients of each mixture component and also their confidence intervals. The amount of information needed to obtain reliable results and its relation to the accuracy of our analysis are discussed.

Analysis of multicomponent mass spectra applying Bayesian probability theory.

In this paper we develop a method for the decomposition of mass spectra of gas mixtures, together with the relevant calibration measurements. The method is based on Bayesian probability theory. Given a set of spectra, the algorithm returns the relative concentrations and the associated margin of confidence for each component of the mixture. In addition to the concentrations, such a data set enables the derivation of improved values of the cracking coefficients of all contributing species, even for those components for which the set does not contain a calibration measurement. This latter feature also allows one to analyze mixtures that contain radicals in addition to stable molecules. As an example, we analyze and discuss the mass spectra obtained from the pyrolysis of azomethane, which contain the radical CH3 apart from nitrogen and C1- and C2-hydrocarbons.

Background estimation in experimental spectra

A general probabilistic technique for estimating background contributions to measured spectra is presented. A Bayesian model is used to capture the defining characteristics of the problem, namely, that the background is smoother than the signal. The signal is allowed to have positive and/or negative components. The background is represented in terms of a cubic spline basis. A variable degree of smoothness of the background is attained by allowing the number of knots and the knot positions to be adaptively chosen on the basis of the data. The fully Bayesian approach taken provides a natural way to handle knot adaptivity and allows uncertainties in the background to be estimated. Our technique is demonstrated on a particle induced x-ray emission spectrum from a geological sample and an Auger spectrum from iron, which contains signals with both positive and negative components.

Reconstruction of surfaces from phase-shifting speckle interferometry: Bayesian approach.

The reconstruction of surfaces from speckle interferometry data is a demanding data-analysis task that involves edge detection, edge completion, and image reconstruction from noisy data. We present an approach that makes optimal use of the experimental information to minimize the hampering influence of the noise. The experimental data are then analyzed with a combination of wavelet transform and Bayesian probability theory. Nontrivial examples are presented to illustrate the proposed technique.

Signal and background separation.

In many areas of research the measured spectra consist of a collection of "peaks"--the sought-for signals--which sit on top of an unknown background. The subtraction of the background in a spectrum has been the subject of many investigations and different techniques, varying from filtering to fitting polynomial functions, have been developed. These techniques yield results that are not always satisfactory and often even misleading. Based upon the rules of probability theory, we derive a formalism to separate the background from the signal part of a spectrum in a rigorous and self-consistent manner. We compare the results of the probabilistic approach to those obtained by two commonly used methods in an analysis of particle induced x-ray emission spectra.

Approach for the evaluation of speckle deformation measurements by application of the wavelet transformation.

We introduce a new, to our knowledge, method using wavelets and probability theory for the evaluation of speckle interference patterns for quantitative out-of-plane deformation measurements of rough surfaces of nontransparent solids. The experiment uses a conventional Twyman-Green interferometer setup. The speckle interference patterns are obtained by the common method of subtraction of images taken before and after a surface deformation. The data are processed by a wavelet transformation, which analyzes the image structures on different length scales. Thus it is possible to separate the interference fringes from the noise. From the locations of the interference fringes, the deformation of the surface can be reconstructed by means of probability theory.